We Rangers hail from back east, what used to be called Nevada. Our heritage stretches back to the days of the Texas Rangers. We learn survival and combat skills in order to go out into the world and have a chance of surviving and making things better.
The Desert Rangers have survived ever since the end of the Great War until their unification with the NCR Rangers in 2271. This small community had a strong survivalist contingent, likely retaining some small arms and books. In the early 22nd century, they clashed with a tribal gang leader in the ruins of Las Vegas. They were known to protect people in cities and towns from enemies such as the White Legs, tribals, and super mutants.
Later, the Rangers came into contact with Caesar's Legion in Arizona and a war ensued. The war was going poorly for the Desert Rangers until, in 2271, NCR Rangers reached the Mojave Wasteland. The Desert Rangers signed the "Ranger Unification Treaty" with the NCR and they were absorbed into the NCR Rangers in exchange for NCR's protection of the Hoover Dam and Nevada from Caesar's Legion. The great monument at the Mojave Outpost remains to this day depicting this historic moment. Certain individuals say that some Desert Rangers still roam the wastes in search for those who prey on the weak.
In Fallout, Tycho mentions that his grandfather was a Desert Ranger, and that his grandfather taught him and his father those survival skills.
In Fallout: New Vegas, there is a monument at the entrance of the "Mojave Outpost" that depicts a Desert Ranger and NCR Ranger shaking hands, representing the pact between the two groups. Veteran Rangers bear a nearly identical appearance to Desert Rangers, suggesting that many of those in their ranks could be former Desert Rangers.
The Desert Rangers are a reference to Wasteland, the 1980s game which Fallout is considered to be the spiritual successor to. That game also featured Desert Rangers facing challenges in a post-apocalyptic setting (specifically, the American Southwest).